Percentage chance of each outcome

Alright this is more of a business problem that I'm encoutering and needed a formula for like yeterday (i.e. urgent)...so I'm just going to simplify it and knowing how to do this I'll know how to do more complex iterations.

A man is playing 5 chess matches and he has X percentage chance to win each game. We know X for each game. Against opponent 1, he has a 25% (.25) chance of winning. Against opponent 2, he has a 45% (.45) chance of winning. Against opponent 3, he has a 55% (.55) chance of winning. Against opponent 4, he has a 75% (.75) chance of winning. And against opponent 5, he has a 95% (.95) chance of winning.

What are his chances of getting 5 wins, 4 wins, 3 wins, 2 wins, 1 win, 0 win? 5 and 0 are easy enough -- .25 * .45 * .55 * .75 * .95 for 5 wins (4.4%) and those numbers subtracted from 1 multiplied by each other for 0 wins (.23%). But I need to know how to do the rest. Who he beats is irrelevent...just need to know the percentage chance of each outcome.

I have no idea if this is a complex or simple problem, but trying to Google how to do this has proven to be fruitless :(